My basement doesn't have adequate light, but I make it work. I have pulled out the DSLR at times, but that has its challenges and doesn't guarantee a better image. A DSLR gives you the opportunity to start with higher quality pixels for post production, but if you don't have the ability to capture a well exposed image (venue is too dark, your lenses aren't fast enough, you aren't allowed to use flash or adjust ambient light, etc.) you aren't going to end up with a much better image from the DSLR.
In my basement I actually prefer to use the cell phone for internet images of my drums. The lens is an ultrawide angle (which helps for confined shots of big things like drums), its aperture if f/1.9 (good luck finding an ultrawide lens with a f/1.9 aperture for a DSLR), it's 16Mp so scaling down reduces noise significantly, and it has a fantastic auto-HDR function so I don't have to use the flash.